ON THE MEAN-VALUE THEOREMS OF Z_(n,k)(s)

One of the authors stated and proved some mean-value theorems for Zn,k (s) . Since he quoted a "theorem" (theorem 74 of) which is erroneous, both the proofs and the theorems have to be modified. The main object of the present paper is to prove the following mean value theorems:     

The Generalization of Ciric and Caristi Type Fixed Point Theorem

In this paper, we generalize the renowned Ciric and Caristi type fixed point theorem and some corollaries. Then we give an example to illustrate our result is really better than the theorem.     

The Relation Between the Generalized Gauss Map and the Classical Gauss Map in the Case of Surface in R

In this paper we prove Theorem 1 in a new way. This theorem directly, gives the relation between the generalized Gauss map and the classical Gauss map in the case of a surface in R~3. By Theorem 1, we can easily deduce an interesting corollary. This corollary covers some results of Hoffman and Osserman.     

Shakedown Analysis of 3-D Structures Using the Boundary Element Method Based on the Static Theorem

The static shakedown theorem was reformulated for the boundary element method (BEM) rather than the finite element method with Melan‘s theorem, then used to develop a numerical solution procedure for shakedown analysis. The self-equilibrium stress field was constructed by a linear combination of several basis self-equilibrium stress fields with undetermined parameters. These basis self-equilibrium stress fields were expressed as elastic responses of the body to imposed permanent strains obtained using a 3-D BEM elastic-plastic incremental analysis. The lower bound for the shakedown load was obtained from a series of nonlinear mathematical programming problems solved using the Complex method. Numerical examples verified the precision of the present method.     

A General Conclusion on Lucas Numbers of the Form px~(2),Where p Is Prime

ABSTRACT． Led。 be the n~(th) Lucas number， n＞0． Let p be an odd prime． In this paper we prove a general theorem． According to the theorem we give an algorithm by using which the equationl-(n)＝px~(2) can be solved for arbitrary given p．Por example，we find its all solutions for 1000＜p＜40000． By the end of the paper an Interestingconjecture Is presented．     

Robustness Proof on A United Watermarking Based on CRT Theorem

A new method of embedding and detecting a joint watermarking is proposed. It applies the asmuth-bloom secret sharing scheme, which is based on CRT (Chinese remainder theorem) theorem, to the digital watermarking technology. On the base of describing the watermarking embedding proceeding and analyzing the watermarking detection proceeding, a series of experiments is done. The experiments emphasize on the method‘s robust proving and security analysis. And the experiments show that the method can resist the attacks of JPEG compress, geometry, noise and gray adjusting. The results of the experiments show that the method has a nice recognition of copyright for joint ownership.     

HARICH-CHANDRA MODULES OVER LIE SUPERAL GEBRAS

In this paper, we obtain a theorem for the classification of the irreducible Harich-Chandra modules over G, Where G is a basic classical Lie superalgebra of I type. And the list of the classi-ficatication is given for G=A(1,0).     

具有一个Lindelf因子的积的正规性(英文)

In this paper a characterization theorem of the normality of products witha Lindel(?)f factor will be proved.The theorem as well as the well known Przym-usinski′s and Rudin′s characterization theorems of the normality of products wi-th a compact factor is a corollary of Theorem 1 below.Throughout this paper we assume that all spaces are T_1.The letterωdenotesthe first infinite cardinal;κ,λdenote the cardinal numbers and other Greek le-     

Existence Theorem of the Multipliers on Riemannian Symmetric Space SL（3,H）／SP（3）

Using the method of Clerc and Stein study the multipliers of spherical Fourier transform on symmetric space to proof the multipliers theory for the space SL(3,H)/SP(3), completely avoid the complex theory of Anker,and we have gain the same result.     

On the Strong Law of Large Numbers for Non-Independent B-Valued Random Variables

This paper investigates some conditions which imply the strong laws of large numbers for Banach space valued random variable sequences. Some generalizations of the Marcinkiewicz- Zygmund theorem and the HoffmannJφrgensen and Pisier theorem are obtained.     

一类分数阶微分方程积分边值问题正解的存在性

In this paper,we concern ourselves with the existence of positive solutions for a type of integral boundary value problem of fractional differential equations with the fractional order linear derivative operator. By using the fixed point theorem in cone,the existence of positive solutions for the boundary value problem is obtained. Some examples are also presented to illustrate the application of our main results.     

Modal extension rule

Modal logics are good candidates for a formal theory of agents. The efficiency of reasoning method in modal logics is very important, because it determines whether or not the reasoning method can be widely used in systems based on agent. In this paper, we modify the extension rule theorem proving method we presented before, and then apply it to P-logic that is translated from modal logic by functional transformation. At last, we give the proof of its soundness and completeness.     

Optimization Problems of the Rank and Inertia Corresponding to a Hermitian Least-Squares Problem

Generally, the least-squares problem can be solved by the normal equation. Based on the projection theorem, we propose a direct method to investigate the maximal and minimal ranks and inertias of the least-squares solutions of matrix equation AXB= C under Hermitian constraint, and the corresponding formulas for calculating the rank and inertia are derived.     

K-quasi-additive fuzzy integrals of set-valued mappings

We first define the quasi-addition and quasi-multiplication operations by introducing the inductive operator, and then, in the K-quasi-additive fuzzy measure space, we establish the K-quasi-additive fuzzy integral of a generally measurable set-valued mapping. Applying the integral transformation theorem, some basic properties of the K-quasi-additive fuzzy integrals with respect to this kind of set-valued mapping are studied. Finally, the generalized monotone convergence theorems of this kind of fuzzy integrals are obtained.     

Optimal Investment of Defined Contribution Pension Based on Self-Protection and Minimum Security

This paper mainly studies the optimal investment problem of defined contribution(DC)pension under the self-protection and minimum security. First, we apply Ito? theorem to obtain the differential equation of the real stock price after discounting inflation. Then, under the constraint of external guarantee of DC pension terminal wealth, self-protection is introduced to study the maximization of the expected utility of terminal wealth at retirement time and any time before retirement. The explicit...     

A THEOREM ON THE CONVEXITY OF PLANAR PARAMETRIC CURVES OF DEGREE N

The main result of this paper is a theorem about the. convexity of curves of degree n on a plane. As its application ,we obtained a sufficient condition that a space curve of degree n in R3 has no singularity points and staying points.     

L~p( [0, 1])-characterizations of multi-knot piecewise linear spectral sequences

There exists a class of new orthonormal basis for L2([0, 1]), whose exponential parts are multi-knot piecewisf linear functions called spectral sequences. In this paper, we show that these bases constitute bases, but not unconditional bases, for Lp([0, 1 ]) with 1相似文献   

THE SARD BEST APPROXIMATION OF LINEAR FUNCTIONAL

In numerical analysis, it is significant to approximate the linear functional Ef=sum from i=0 to m-1([integral from a to b(a_1(x)f~(1)(x)dx+ sum from f=0 to i_1(b_1f~(1)(x_1))]) by a simpler linear functional Lf=sum from i=1 to m(a_1f(x_1)) In this paper, making use of natural Tchebysheff spline function, we give existence theorem and uniqueness theorem of L that is exact for the degree m to F; we also give three sufficient and necessary conditions in which L is the Sard best approximation to F.     

On the Symmetry Classes of Functions

Let R be an integral domain of characteristic zero such that the corresponding group rings have block decompositions. We first prove that the submodule consisting of all the R-valued ξi-symmetric functions of several variables is a symmetry class, where ξi is any block character. Then we present a relationship among certain operators introduced for block character. Then we present a relationship among certain operators introduced for block characters. As a consequence, we obtain a decomposition of an arbitrary R-valued function of several variables. Finally, we describe the symmetry property of such summands and determine all the symmetry classes.     

An improvement of Papadakis'' theorem

There exist many orthonormal wavelets which cannot be derived by multiresolution analysis (MRA) with a single scaling function.In 2000,Papadakis announced that any orthonormal wavelet is derived by a generalized MRA with countable scaling functions at most.We improve Papadakis' theorem and find that for any othonormal wavelet,the least number of the corresponding scaling functions is just the essential supremum of the dimension function of the orthonormal wavelet.Moreover,we construct directly the fewest scaling functions